Resoudre dans R l'équation (2x-3)²=(4x-7)² l'inequation 6/(x-3) ≥ 2x-2

[tex](2x-3)^2=(4x-7)^2\\ (2x-3)^2-(4x-7)^2=0\\ (2x-3-4x+7)(2x-3+4x-7)=0\\ (-2x+4)(6x-10)=0\\\\ -2x+4=0\\ -2x=-4\\ x=2\\\\ou\\\\ 6x-10=0\\ 6x=10\\ x= \frac{10}{6}= \frac{5}{3} \\\\\\\\ [/tex]



[tex] \frac{6}{x-3} \geq x-2 \\\\ 6 \geq (x-2)(x-3)\\ 6 \geq x^2-5x+6\\ x^2-5x \leq 0\\ x(x-5) \leq 0\\\\ x \leq 0\\\\ou\\\\ x-5 \leq 0\\ x \leq 5[/tex]